ques no 18 with explaination
ques no 18 with explaination 14. Which of the following is dimensionally inco 2 (I) u = v — at (4) v2 — u2 = 2as u2 = 2a (gt — 1) 15. 1 joule of energy is to be converted into new system of units in which length 10 metre, mass in 10 kg and time in 1 minute. The numerical value of I J in the new syste.n (2) 36 x 10-3 (1) 36 x 10-4 (4) 36 x 10-1 (3) 36 x 10-2 16. If the unit of force is 1 kilo newton, the length is 1 km, and time is 100 second what '"II be (1) 1000 kg (4) 100 kg (3) 10000 kg 17. The imensional formula for moment of couple is [ML2T-2] (3) [ML-1T-3] (2) [MLT-21 (4) [ML-2T-2] 18. The potential energy of a particle varies with distance x from a fixed origin as , where A and B are dimensional constants then dimensional formula for ABE 5,2+B (1) [ML7/2T-2] (3) [M2L9/2T-2] (2) [ML1112T-21 (4) [ML1312T-31 19. Of the following quantities which one has dimensions different from the remaining three?

Dear student

U=Axx2+B...11)As x2 is added to B so as like terms has the same dimension.dimension of B=L22)Dimension of denomenator is =L2U=Axx2+BU=AxL2A=U×L2xA=ML2T-2×L2LA=ML(4-12)T-2A=ML72T-2Dimension of AB=ML72T-2×L2Dimension of AB=ML(72+2)T-2Dimension of AB=ML112T-2Regards

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Ok so , one thing to notice is that U - potential energy and the dimensional formula of any kind of energy is one and the same = [ML2T-2]

Now see that the term 'B' is being added to x2  - square of distance - with dimensional formula of [L2]
Only like terms can be added. That is distance2 can be added to distance2 only, neither can it be added to distance or distance3 , nor can it be added to some other qty altogether like pressure or force etc.

So we now know that B has D.F = [L2]

Now solving Ax1/2/x2 = Ax-3/2. - whic technically should be equal to energy D.F

So solving on both sides we get A = [ML7/2T-2]

AB = [ML7/2T-2][L2] = [ML11/2T-2] .

Hence option(2)

Hope this helped !:))
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